1 2 3 4 5 Quasi-Newton inversion of seismic first arrivals using source finite bandwidth assumption: application to landslides characterization from velocity and attenuation fields. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Julien Gance (1,2), Gilles Grandjean (1), Kévin Samyn (1) and Jean-Philippe Malet (2) 23 Keywords: 24 25 Inverse theory, Seismic tomography, Fresnel wavepaths, Finite frequency, Resolution improvement, Landslide 26 27 28 29 30 31 32 33 (1) BRGM, Bureau de Recherches Géologiques et Minières, 3 Avenue Claude Guillemin, F-45060 Orléans, France (2) Institut de Physique du Globe de Strasbourg, CNRS UM7516, EOST/Université de Strasbourg, 5 rue Descartes, 67084 Strasbourg Cedex, France. Corresponding author: Julien GANCE BRGM, Natural Hazard Department. 3 Avenue Claude Guillemin BP36009 45060 Orléans Cedex 2, France Phone : +33 (0)2 38 64 38 19 Fax : +33 (0)2 38 64 35 49 E-mail address: j.gance@brgm.fr 34 1. Introduction 35 36 Near-surface geophysical techniques are of great potential to image subsurface structures in many 37 geomorphological studies (Schrott and Sass, 2008; van Dam, 2010), and even more specifically for 38 improving the knowledge on landslide features (Jongmans and Garambois, 2007). Landslide analysis 39 generally involves the combined use of several geophysical methods to image different petrophysical 40 parameters (Bruno and Marillier, 2000; Mauritsch et al., 2000; Méric et al., 2011). Seismic surveys are 41 particularly well adapted to detect and characterize specific features of landslides such as spatial 42 variation in compaction and rheology of the material (Grandjean et al., 2007), variation in fissure 43 density at the surface (Grandjean et al., 2012), and complex slip surface geometries (Grandjean et al., 44 2006). As the wave propagation is mainly controlled by the elastic properties of the medium, seismic 45 surveys are often well correlated with geotechnical observations. 46 Among them, different approaches can be used for processing data depending on the analysis of 47 the different kind of waves associated to particular propagation phenomena. Bichler et al. (2004) and 48 Bruno and Marillier (2000) interpreted the late arrivals of P-waves to image the bedrock geometry 49 using seismic reflection analysis. Mauristch et al. (2000) and Glade et al. (2005) analyzed refracted 50 waves to define the internal geometry (e.g. layering) of the landslides. Grandjean et al. (2007) and 51 Grandjean et al. (2011) studied the first arrival traveltimes to recover P-wave velocity distribution 52 across landslides. More recently, Samyn et al. (2011) used a 3D seismic refraction traveltime 53 tomography to provide a valuable and continuous representation of the 3D structure and geology of a 54 landslide. Grandjean et al. (2007) and Grandjean et al. (2011) used also Spectral Analysis of Surface 55 Waves (SASW) techniques to obtain S-wave velocity distributions along landslide cross-sections. 56 Finally, based on the work of Pratt (1999) and Virieux and Operto (2009), Romdhane et al. (2011) 57 demonstrated the possibility to exploit the entire wave signal by performing a Full elastic Waveform 58 Inversion (FWI) on a dataset acquired on a clayey landslide. 59 These methods are based on more or less important assumptions on the soil type and their 60 petrophysical characteristics, on the complexity of layers, and on their geometry, and are therefore not 61 recommended for all case studies. Seismic refraction can be basically performed using the General 62 Reciprocal Method (GRM; Palmer and Burke-Kenneth, 1980) or the Plus/Minus Method (Hagedoorn, 63 1959). These methods are fast and easy to implement, but mostly based on simple hypotheses - such as 64 a layered media - and are consequently not very efficient to recover important variations in lateral 65 velocity. Reflection surveys need to record high frequency waves to obtain a good resolution of final 66 stacked sections; they are difficult to set up for subsurface applications because of the strong 67 attenuation affecting high frequencies and decreasing the signal to noise ratio (Jongmans and 68 Garambois, 2007). Moreover, this method produces a reflection image that cannot be directly and 69 easily interpreted as direct information on the mechanical properties of the medium that could be 70 derived from velocity fields. FWI appears to be the more advanced method since it is based on the 71 realistic assumption of an elastic media and uses the whole seismic signal in the inversion scheme. 72 However, it remains a complex method, requiring an important data pre-processing (source inversion, 73 amplitude correction, initial model estimation) that is hardly applicable to near surface real data 74 featured with a low signal to noise ratio and complex waves interactions (Romdhane et al., 2011). As a 75 consequence, the issue of recovering the structural image of a landslide from the seismic velocity field 76 estimated with an accurate method is still a challenge. 77 The objective of this work is to refine the first arrival tomography approach applied to landslide 78 analysis, which is a good compromise between the strong assumptions made in simple refraction 79 methods and the complexity of the FWI approach when used in very heterogeneous soils. P-wave 80 tomography is largely used, from crustal to shallow geotechnical studies and allows recovering, at a 81 relatively low cost, a reliable image of the velocity distribution. In this perspective, Taillandier et al. 82 (2009) proposed to invert first arrival traveltime tomography using the adjoint state method, but had to 83 face the problem of gradient regularization. The proposed method is based on a Hessian formulation 84 (Tarantola, 1987) to ensure an optimum convergence of the velocity model during iterations. We only 85 use here the first arrivals of the seismic signal caused by direct or refracted waves. In that case, late 86 arrival, including scattering, conversion effect are not taken into account in the inversion. 87 In the next section, we detail the theory used to formulate the inversion equation and the related 88 approximations introduced for optimizing the algorithm and ensuring the convergence toward the best 89 solution. The final algorithm is tested on a synthetic case in order to estimate the quality of the 90 velocity field reconstruction without considering noisy data. To compare our results with a reference 91 case, the synthetic velocity model is identical to the one used by Romdhane et al. (2011). Then, we 92 process a real seismic dataset obtained from a seismic survey at the Super-Sauze landslide (South 93 French Alps) in clayey material. On this case study, we invert for the P-wave velocity field but also for 94 the attenuation factor. The effects of noisy data on the quality of the reconstructed velocity field are 95 analyzed, and the observed surface variation in the velocity field is discussed by integrating other 96 sources of information (geotechnical tests and geomorphological interpretation). 97 98 99 2. Theoretical approach a. General inverse problem 100 Solving the inverse problem requires a modeling step (e.g. the direct problem) for computing the 101 residuals (e.g. the difference between computed and observed data). An updated model can be 102 estimated by back-projecting the data residuals on each cell of the model discrete grid. The direct 103 problem thus consists in finding a relation between the data t, taken here as the first arrival traveltimes, 104 and the physical P-wave velocity model s, such as: 105 π‘ = π(π ) (1) 106 107 This problem is generally solved using the asymptotic high frequency wave propagation 108 assumption in a non-homogeneous isotropic medium. The wave propagation equation is then 109 simplified into the eikonal equation that computes the first arrival traveltimes over a discrete grid for 110 example by using a finite-difference scheme (Vidale, 1998). This technique has been improved for 111 sharp velocity contrasts (Podvin and Lecomte, 1991), optimized by Popovici and Sethian (1998) who 112 proposed the Fast Marching Method (FMM), by Zhao (2005) who proposed the Fast Sweeping 113 Method, and recently adapted to non-uniform grids (Sun et al., 2011). The technique is actually largely 114 used because of its efficiency and accuracy. In this study, we use the FMM algorithm (Popovici and 115 Sethian, 1998) to compute the direct problem. The computation of the first arrival traveltime is 116 generally followed by a ray tracing that uses the traveltimes maps to propagate the wavepath from the 117 sources to the receivers. The traveltime t can then be expressed using the following matrix form: π‘ = πΏπ (2) 118 119 where L is the length of the ray segment crossing each cell of the slowness model S. Generally, the 120 Fermat principle allows the Fréchet derivatives matrix to be approximated by the matrix πΏ (Baina, 121 1998). This principle establishes that a small perturbation πΏπ on the initial model does not change the 122 ray paths, and therefore, only affect the traveltime πΏπ‘ at the second order. This linearization of the 123 problem around the slowness model π π implements the Quasi-Newton (Q-N) assumption and makes 124 the resolution of the nonlinear problem to be solved by the following tomographic linear system: 125 [(πΏπ )π πΏπ ]πΏπ = [(πΏπ )π πΏπ‘] (3) 126 127 where k and T represent respectively the iteration index and the transpose operator. Several 128 techniques can be used to solve Eq. 3. The Simultaneous Iterative Reconstruction Technique (SIRT) is 129 the most common because it does not require a large computer memory; consequently, SIRT is widely 130 used to invert large sparse linear systems (Trampert and Leveque, 1990). Its convergence toward a 131 least-square solution has been proved (Van der Sluis and Van der Vorst, 1987) but this method suffers 132 from few drawbacks: SIRT introduces an intrinsic renormalization of the tomographic linear system 133 that modifies slightly the final solution. For that reason, we propose to use in our approach the LSQR 134 (Least-Square QR) algorithm (Paige and Saunders, 1982) that has been proved to be superior to SIRT 135 or Algebraic Reconstruction Techniques ART algorithms in terms of numerical stability and 136 convergence rates (Nolet, 1985). 137 b. From rays to Fresnel volumes 138 Revisiting seismic traveltimes tomography also needs to consider the ray approximation, e.g. the 139 infinite spectral bandwidth assumption. The main issue of this approximation lies in the traveltime 140 computation taken as line integrals along the rays spreading over the slowness model. Because the 141 slowness values are only considered along ray paths, the problem is often underdetermined and leads 142 to numerical instability (Baina, 1998). In practice, this difficulty is generally by-passed using 143 regularization operators to reduce the non-constrained part of the model, and then, to reinforce the 144 numerical stability. Generally, a simple smoothing of the reconstructed slowness model (Zelt and 145 Barton, 1998), the application of a low-pass filter on the gradient (Taillandier, 2009) or the elimination 146 of the lowest eigenvalues in the Hessian matrix (Tarantola, 1987) can be used. However, such 147 regularization operators require the selection of appropriate parameters (filter length, eigenvalue cutoff 148 and more generally the size and weights of the smoothing operators). Kissling et al. (2001) 149 demonstrated the dependency of these parameters on the resolution and the quality of the final model 150 in poor wavepath coverage areas. This is the reason why the use of physically-based regularization 151 operators such as Fresnel volumes or sensitivity kernels is preferable since they are based on non- 152 subjective principles completely defined by the problem. 153 With this assumption, several methods have been developed including those using the concept of 154 Fresnel volumes as a regularization factor. Nolet (1987) proposed to use the size of the Fresnel zone to 155 constrain the size of a spatial smoothing operator. Vasco et al. (1995), Watanabe et al. (1999), 156 Grandjean and Sage (2004) or Ceverny (2001) use the Fresnel volume in the back projection of the 157 residuals. 158 More recently, the concept of sensitivity kernels or Fréchet Kernel introduced by Tarantola (1987) 159 has been reformulated for traveltime tomography. It represents a good compromise between the strong 160 assumption of the asymptotic ray theory and the high computational cost of the complete full wave 161 inversion tomography (Liu et al., 2009). While ray theory is well adapted in media characterized by 162 geological structures larger than the first Fresnel zone, the use of sensitivity kernels allows to 163 overcome this constraint and then, to increase the spatial resolution (Spetzler and Snierder, 2004). 164 Several authors have developed this concept and investigated the properties of the sensitivity kernels 165 for traveltime tomography in homogeneous media, mainly at the spatial scale of the earth crust 166 (Dahlen et al., 2000; Dahlen, 2005; Zhao et al.; 2006). The strategies proposed by these authors are 167 generally limited to smoothly heterogeneous media (Liu et al., 2009; Spetzler et al., 2008) and are 168 barely applied to real datasets, mainly because of prohibitive calculation costs (Liu et al., 2009). 169 Sensitivity kernels and Fresnel volumes are constructed on the single scattering (Born) 170 approximation. This approximation considers that a part of the wave can be delayed by velocity 171 perturbation in the vicinity of the ray path. For highly heterogeneous media, this approximation is not 172 valid anymore because multiple scattering should be taken into account to fully explain observed first 173 arrivals. 174 In the particular case of subsurface soil investigation where highly heterogeneous media are 175 observed, the use of sensitivity kernels is not recommended since it would involve complex algorithms 176 and computing times similar to those featuring the FWI approach. In this context, we decided to solve 177 empirically the problem of complex multiple scattering inside the first Fresnel zone, this approach 178 allowing to address issues of regularization by using increasing finite frequencies bandwidths. 179 Therefore, the developed algorithm assumes that high spatial heterogeneities of the soil around the 180 Fresnel wavepath affect, through complex multiple scattering, the first arrivals of the signal. 181 In the next section, we explain how the Fresnel volumes are defined as a simplification of the 182 sensitivity kernels and implemented in a Q-N algorithm. 183 184 We first express the Fresnel weights proposed by Watanabe et al. (1999) and used by Grandjean and 185 Sage (2004), in order to materialize the wavepath in the model. They classically decrease linearly from 186 a value of one (when the cell is positioned on the ray path) to a value of zero (when it is out of the 187 Fresnel volume): 188 1 − 2πΔπ‘, π= { 0, 0 ≤ Δπ‘ < 1 ≤ Δπ‘ 2π 1 2π (4) 189 190 Watanabe et al. (1999) and Grandjean and Sage (2004) defined these weights ω as the probability 191 that a slowness perturbation delay the arrival of the wave by a Δt, where f is the considered frequency 192 of the wave. This definition is interesting because of its simple expression that allows fast computing 193 while taking into account the global shape of the 2D traveltime sensitivity kernel given of Spetzler and 194 Snieder (2004), corresponding to a decrease of sensitivity until the first Fresnel zone. 195 Because the size of the Fresnel volume is depending on the considered source frequency, a new 196 inversion strategy based on increasing frequency can be proposed. To consider the entire source 197 frequency content, some authors compute wavepaths in a band-limited sensitivity kernel, stacking the 198 monochromatic kernels with a weight function similar to the amplitude spectrum of the wavelet 199 (Spetzler and Snieder, 2004; Liu et al., 2009). From our side, we propose to compute the Fresnel 200 weights for a monochromatic wave, increasing its frequency at each step of the inversion. The 201 considered frequency sampling with an increasing rule ranging from the lower to the higher frequency 202 of the source signal. We also choose to give the same weight to all frequencies in order to limit the 203 number of iteration and to preserve the rapid convergence of the algorithm. Taillandier et al. (2009) 204 showed that this method, applied on the gradient filtering permit to overcome the non-linearity of the 205 problem. For low frequency values, the Fresnel zone will be wider and the slowness model will be 206 reconstructed with large wavelengths. Conversely, for high frequency values, the Fresnel zone will be 207 thinner and the slowness model will be reconstructed with sharp wavelengths. This strategy appears 208 efficient to improve the resolution during the inversion - and so the convergence of the algorithm - in 209 full wave inversion where it prevents from cycle-skipping issues (Sirgue and Pratt, 2004; Virieux and 210 Operto, 2009; Romdhane, 2011). Recovering slowness variations whose sizes are in agreement with 211 each wavelength transmitted by the source should lead to better images of local heterogeneities while 212 preserving the algorithm convergence. 213 With these assumptions, the traveltime perturbation can be expressed as the integral over a Fresnel 214 volume multiplied by the slowness perturbation field observed for all points r in the volume (Liu et al, 215 2009). This linear relationship among traveltime and slowness perturbation is the result of the first 216 Born approximation that is only valid for small perturbation (Yomogida, 1992): 217 πΏπ‘ = ∫ π(π)πΏπ (π)ππ (5) 218 219 where π is the Fresnel weight operator (Fig. 1) normalized by the area of the Fresnel ellipse 220 perpendicular to the raypath π, for each shot and receiver such as: 221 π(π) = 1 π(π) π (6) 222 223 This normalization allows linking our approach to the geometrical ray theory in the case of a plane 224 wave propagation (Vasco et al, 1995; Spetzler and Snieder, 2004; Liu et al, 2009), so that the integral 225 of W over a surface perpendicular to the wavepath is equal to one, which is generally verified for 226 sensitivity kernels: 227 +∞ ∫ π(π , π, π)ππ = 1 (7) −∞ 228 229 The Fresnel volume thus defined, also called Fréchet kernel corresponds to the Fréchet derivative 230 (Yomogida, 1992; Tarantola, 1987) or Jacobian matrix of the forward problem, similar to the length of 231 ray segment matrix πΏ defined in the asymptotic ray theory. The problem, considered in 2D, can then 232 be written in its matrix form (Vasco et al, 1995): 233 πΏπ‘ = π πΏπ (8) 234 235 where π is the [number of data x number of cells] Fresnel weight matrix, calculated for each shot and 236 for each receiver such as for the cell j and for the couple source-receiver i: 237 πππ = πππ π 238 239 where π is the length of the Fresnel surface along a direction perpendicular to the ray path. (9) 240 We are however aware that the use of the Fresnel weight as defined previously is a rough 241 approximation of the wavepath. This is the reason why we prefer to keep the ray assumption to 242 compute traveltimes, avoiding the introduction of any error due to this approximation. This choice has 243 been justified by Liu et al. (2009) who observed small differences between traveltime values computed 244 with both approaches. 245 246 c. New implementation of the inverse Problem 247 In the previous section, we showed that the Born approximation combined with Fresnel volumes 248 allowed the estimation of Fréchet derivative. To solve the nonlinear inverse problem, we use a steepest 249 descent iterative algorithm to minimize the πΏ2 norm misfit function l (Tarantola, 1987) that can be 250 written in this particular case: 251 π(π ) = 1 π [(π(π ) − π‘πππ )π πΆπ−1 (π(π ) − π‘πππ ) + (π − π πππππ ) πΆπ−1 (π − π πππππ )] 2 (10) 252 253 where πΆπ and πΆπ are respectively the covariance operators on data and model, π represents the 254 theoretical relationship between the model π and the traveltimes π‘, π‘πππ the observed data and π πππππ 255 the a priori information on the model. 256 The Q-N method consists in minimizing the misfit function iteratively using its gradient and 257 approximated Hessian matrix. The gradient gives the direction of steepest descent of the misfit 258 function while the Hessian matrix is used as a metric indicating its curvature, approximated locally by 259 a paraboloïd (Tarantola, 1987). Compared to the gradient method, the Hessian is here used to improve 260 the assessment of direction and norm of the update vector that is applied to the slowness model, so that 261 each step is performed in the good direction and with an optimized length. The tomographic linear 262 system in the case of no a priori information on the model can be written in its matrix form: 263 [(π π )π πΆπ−1 (π π )] πΏπ = [(π π )π πΏπ‘] 264 (11) 265 This linear tomographic system can be solved by using a LSQR algorithm. The Fresnel weights 266 matrix employed is a [number of data x number of cells] matrix. Its computation is straightforward on 267 classical personal computers. The Q-N algorithm is based on the inverse of the Hessian matrix that is a 268 square matrix of size [number of data x number of data] that can be difficult to invert for large dataset. 269 In our case, we used cluster computing to invert our data and optimized the step size along the 270 direction given by the Hessian using a scalar to weight the slowness update thanks to a parabolic 271 interpolation (Tarantola, 1987). 272 273 d. Validation on a synthetic dataset 274 To compare the performance of our algorithm with full wave inversion, it was tested on the synthetic 275 transverse section used by Romdhane (2011) representing a typical cross-section of a landslide (Fig. 276 2a). The performance of the method is discussed by taking as a reference the SIRT algorithm of 277 Grandjean and Sage (2004). 278 The synthetic dataset has been calculated with a simple 2D eikonal equation solver, so that traveltimes 279 are not perturbed by scattering effects. The dataset is composed of 50 shots recorded on 100 280 geophones. The model consists in 209x68 cells of 1 m in width. The seismic sources are spaced 281 regularly every 2 m and the geophones every 1 m. The synthetic model is composed of ten layers with 282 P-wave velocity ranging from 110 m.s-1 to 3300 m.s-1. It represents a transversal cross-section of the 283 landslide body lying on a homogeneous consolidated bedrock. Except between the landslide body and 284 the bedrock, the changes in P-wave velocity are small, so that it is difficult to reconstruct the detailed 285 shape of the landslide body. The stopping criterion is a change in the cost function lower than 1% and 286 the inversion is limited to 20 steps. 287 Figure 2b and 2c compare the results obtained with the SIRT algorithm (Grandjean and Sage, 2004) 288 and the Q-N one. They converge respectively in 15 and 20 iterations. The convergence of the misfit 289 function is better for the Q-N algorithm with a value 3.6 times lower than the SIRT. Globally, the Q-N 290 algorithm succeeds in recovering the shape of the bump at 2000 m.s-1 located on the left side of the 291 cross-section and renders a more spatially detailed shape of the bedrock topography (Fig. 2b, 2c). The 292 SIRT algorithm does not retrieve those initial structures. We can notice that both algorithms have 293 difficulties to reproduce the low velocity of the very near surface layer, because of the poor ray 294 coverage occurring in this area. 295 Figure 2d, 2e and 2f compare the results on three vertical cross-sections chosen to highlight the ability 296 of the algorithm to recover P-wave velocity with a better accuracy than the SIRT. We can notice that 297 for the top-soil, P-wave velocity are the same for both algorithms and are equal to the P-wave 298 velocities of the initial model in that zone. Moreover, The Q-N algorithm seems to be able to recover 299 lowest wavelengths than the SIRT one as on figure 2d between 55 and 60 m of depth. 300 This synthetic example demonstrates the ability of the Q-N algorithm to recover the shape of the 301 internal layers of a landslide body. Contrary to the SIRT result, the Q-N allows to interpret correctly 302 the thickness and geometry of the different layers. 303 304 305 3. Application of the Q-N algorithm on a real dataset a. Study site presentation 306 The Q-N algorithm has been applied on a real dataset acquired at the Super-Sauze landslide (South 307 French Alps). The landslide has developed in Callovo-Oxfordian black marls. Its elevation is between 308 2105 m at the crown which is established in in-situ black marls covered by moraine deposits and 1740 309 m at the toe. The landslide is continuously active with displacement rates of 0.05 to 0.20 m.day-1 310 (Malet et al., 2005a). The detachment of large blocks of marls from the main scarp (Fig. 3) and their 311 progressive mechanical and chemical weathering in fine particles explain the strong grain size 312 variability of the material especially in the topsoil (e.g. decametric blocks of marls at various stages of 313 weathering, decimetric and centimetric clasts of marls, silty-clayed matrix; Maquaire et al., 2003). The 314 bedrock geometry is complex with the presence, in depth, of a series of in-situ black marl crests and 315 gullies, partially or totally filled with the landslide material (Flageollet et al., 2000; Travelletti and 316 Malet, 2012). This complex bedrock geometry delimits sliding compartments of different 317 hydrogeological, rheological and kinematical pathways. The variable displacement rates and the 318 bedrock geometry also control the presence of large fissures at the surface (Fig. 3b, 3c) that can be 319 imaged with joint electrical and electromagnetic methods (Schmutz et al., 2000). Many kinds of 320 heterogeneities are observed at different scales, and they control directly the mechanical behavior of 321 the landslide by creating excess pore water pressures (Van Asch et al., 2006; Travelletti and Malet, 322 2012). The top soil surface characteristics have also a large influence on the surface hydraulic 323 conductivity (Malet et al., 2003) and therefore, on the water infiltration processes (Malet et al., 2005b; 324 Debieche et al., 2009). In this context, we tested the Q-N P-wave tomography inversion scheme to 325 provide a high-resolution characterization of structures and detect small scale heterogeneities along a 326 N-S transect of the landslide. 327 328 b. P-wave velocities inversion 329 330 The seismic profile is parallel to the main sliding direction of the material, and is located in the upper 331 part from the secondary scarp to the middle part of the accumulation zone (Fig. 3). The base seismic 332 device has a length of 94 m long and consisted of 48 vertical geophones (with a central frequency of 333 10 Hz) regularly spaced every 2 m. The 60 shots have been achieved with a hammer every 4 m. We 334 used a roll-along system to translate the acquisition cables with a 24 geophones overlap and then 335 investigate a 238 m long linear profile. The recording length is 1.5 s with a sample rate of 0.25 ms and 336 the acquisition central consists in a Geometrics Stratavizor seismic camera (48 channels). The shots 337 show a relatively good signal to noise ratio until the last geophone in the upper part of the section. The 338 shots of the lower part are affected by the higher density of soil fissures. The attenuation and the signal 339 to noise ration are consequently higher in this part of the profile. The signal is dominated by the 340 surface waves but the first arrivals are clearly visible for all seismic shots. 341 342 343 344 To estimate the pick uncertainty, the time difference of the picks from reciprocal source-receiver pairs 345 was examined. Two different people picked the first arrival of the waves, and for each created dataset 346 we studied the difference between reciprocal traveltimes. From each dataset, we created 3 subsets: a 347 first one kept intact, a second one where we corrected the picks having more than 10 ms of difference 348 in traveltime reciprocity, the picks being removed when not possible and a third one removing picks 349 having a difference of traveltime reciprocity greater than 10 ms. We inverted the 6 datasets and kept 350 the one which gave the lower final misfit function value and the P-wave tomogram the most reliable 351 with our a priori knowledge of the studied zone. The differences between P-wave tomograms were not 352 so important, but the dataset selected permitted to interpret the results unequivocally. The error in 353 reciprocity of traveltimes can be approximated by a Gaussian belt with a standard deviation of 2.2 ms 354 (Fig. 5). 355 356 The inversion has been performed with the Q-N algorithm on a 358 x 153 grid. Each square cell of 357 the grid measures 0.67 m. The hammer source gave frequencies comprised between 30 Hz and 120 Hz 358 with a dominant frequency of 40 Hz. Those frequencies are also present in the P-wave up to the end of 359 the profile (Fig. 4b). Regarding the different amplitude spectra, we considered those values as constant 360 for each shot. For the first iteration, the frequency was set to 30 Hz and then increases at each step to 361 respectively 45 Hz, 60 Hz, 75 Hz, 90 Hz, 105 Hz and 120 Hz; after the eighth steps, the frequency was 362 kept constant at 120 Hz. 363 364 365 The initial model is of a first importance for a good convergence. Indeed, the linearization of the 366 problem around the initial model is only valid for model close to the real one. This reason motivates 367 the automated calculation of the initial model from the data by using a simplified slant-stack algorithm 368 transforming the dataset in the velocity - intercept times domain. Then, theoretical traveltime curves 369 were calculated in a double loop for a velocity v ranging from π£πππ to π£πππ₯ (defined by the user) and 370 for a range of intercepts π such as: 371 π‘=π+ 372 ππππ ππ‘ π£ (12) 373 For each of these theoretical curves, the model was compared to the observed traveltimes; the 374 number of points with a difference of less than 0.5 ms was stored in the π-p plan (Fig. 6a). For each 375 intercept, the velocity corresponding to the maximum number of point was used to create a profile of 376 velocity that is further used under the shot point (Fig. 6b). 377 The depth π corresponding to each velocity was then deduced from the velocities by using Eq. 13: 378 π(π) = π(π − 1) + π£(π) ∗ πΏπ‘ (13) 379 380 where πΏπ‘ represents the sample rate of intercepts (Fig. 6c). 381 The velocity profiles were gathered to form the initial model that was finally smoothed to 382 avoid lateral artifacts. With a misfit function value of 0.3612, this initial model is supposed to be as 383 much as possible close to the final one which is the best way to avoid divergence or convergence in 384 local minimum. The stopping criterion was set to a percentage change lower than 1 % and the number 385 of iteration was limited to 20. The misfit function value associated to the final model is 0.0122 and has 386 been obtained after 17 iterations. Figure 7 shows the misfit functions related to the Q-N and SIRT 387 algorithms for comparison. 388 Figure 8 shows respectively the initial velocity model and the inverse models obtained with both SIRT 389 and Q-N algorithms. 390 391 c. Seismic wave attenuation tomography 392 393 The amplitude of the first arrival is exploited here to image the wave attenuation. Seismic wave 394 attenuation is an efficient physical property because it is directly linked to porosity and to the presence 395 of fissures in the media (Schön, 1976). Several attenuation parameters can be used to invert seismic 396 attenuation: spectral ratio, centroid frequency shift and peak frequency shift (De Castro Nunes et al., 397 2011). In our analysis, we used the simple method proposed by Watanabe and Sassa (1996) 398 considering that in a homogeneous attenuation media the amplitude of the spherical wave verifies: π΄(π) = π΄0 −πΌπ π π (14) 399 400 where π΄0 is the amplitude of the source signal, r the distance from the seismic source along the 401 raypath and α the attenuation coefficient. 402 Applying a logarithm function, the equation becomes linear in πΌ. We proposed to compute the 403 attenuation tomography after the P-wave velocity field so that the problem is reduced to a simple 404 linear problem: πΌ = πΌ + π π πΏπ΄ (15) 405 406 where α is the attenuation coefficient, πΏπ΄, the amplitude update and W the Fresnel weights matrix. 407 We performed five iterations starting from a simple homogeneous media with an attenuation πΌ = 408 1.0 π −03 Np.m-1 and calculated the Fresnel weights matrix for the Q-N inverted Vp model and for five 409 frequencies (30 Hz, 45 Hz, 60 Hz, 90 Hz, 120 Hz). Although the results are generally presented 410 through the dimensionless quality factor, in our case, the dominant source frequency is almost constant 411 for each shot (40 Hz) and the raw results are more contrasted. Moreover, because the definition of the 412 quality factor can be different for lossy (highly attenuating) materials (Schön, 1976), we image 413 directly the attenuation map. In order to compare the attenuation map with surface fissuring, a 414 geomorphological inventory of the fissures was created by direct observations in the field along the 415 seismic profile. All the fissures of width larger than 0.05 m were mapped. The Surface Cracking Index 416 (SCI), defined as the total length of fissures per linear meter of the seismic profile, is represented in 417 Figure 9a. 418 419 420 421 4. Interpretation and discussion 422 The velocity model is firstly compared to the geometrical model proposed by Travelletti and Malet 423 (2012) proposed from the integration of multi-source data (e.g. electrical resistivity tomographies, 424 dynamic penetration tests and geomorphological observations) at coarser scale. 425 The bedrock depths obtained from penetration tests were used to deduce the minimum velocity of the 426 bedrock fixed at 850 m.s-1. The bedrock position thus obtained is compared to the one of Travelletti 427 and Malet (2012) along the profile (Fig. 10a, b). The thickness was calculated for both models with the 428 topography observed in 2011. The depth interval observed is the same (2 to 13 m) and the global 429 shape of the bedrock is identical. The main differences are lower than 4 m and are located downhill of 430 the profile, from the abscissa 100 to 230 m where the bedrock topography is more complex. It shows 431 important high frequencies variations that are less pronounced on the topography from Travelletti and 432 Malet (2012). 433 434 To assess the quality of the Q-N algorithm result, we compare the bedrock depth variation with the 435 topography visible on a black and white orthophotograph of 1956 before the landslide (e.g. when the 436 original relief was not covered by the landslide material). The figure 11a shows the orthophotograph 437 of 1956 overlaid on the digital elevation model available for the same date. The seismic profile is also 438 represented. We can notice on the picture the very irregular geometry of the relief composed of 439 alternating crests and gullies of different sizes. The studied profile crosses different geometries. From 440 the point A to B (Fig. 11a), the topography seems first regular, before crossing a large thalweg. After 441 crossing this thalweg, the profile goes across a long transversal crest that forms a bump and then, 442 plunges along the downstream slope. Those patterns are also present in the P-wave tomogram, 443 respectively at 125, 140 m and 160 m. 444 Near the abscissa 180 m, a zone of low velocities (< 900 m.s-1) is observed in depth that can be 445 interpreted as an old small-sized gully, also visible as a black dot on the orthophotograph. 446 447 From this observation, we constructed an interpreted geological model that gathers geophysical and 448 geomorphological information (Fig. 11b). This model is composed of three different materials. The 449 first one is the Callovo-Oxfordian intact black marls that constitute the bedrock, characterized by 450 velocities greater than 3000 m.s-1 (Grandjean et al., 2007) and with a topography following the one 451 visible on the DEM from 1956. The second one is the unconsolidated material that presents P-wave 452 velocities between 400 and 1200 m.s-1, characteristic of unconsolidated deposits (Bell, 2009). It 453 constitutes the active unit of the landslide, e.g. the layer that presents most displacements. The third 454 material, characterized by an interval of velocities between 1500 and 2500 m.s -1 is interpreted as 455 compacted landslide material, because it is only present at a higher depth, where the height of soil 456 above is sufficient to compact the landslide deposit. This layer is not involved in the dynamics of the 457 landslide and is quasi-impermeable (Malet, 2003; Flageollet et al., 2000; Travelletti and Malet, 2012). 458 459 Now that we proved the reliability of the Q-N algorithm tomography to recover the paleotopography, 460 we can assess its contribution by comparing this result from the SIRT tomography of Grandjean and 461 Sage (2004). We can notice on figure 8b and 8c, that the upper part of the profile (between the 462 abscissa 0 and 100 m) presents a smoother contrast between the active unit and the bedrock for the 463 SIRT result. Although two bumps are visible at the abscissa 100 and 140 m, the large in-between 464 depression is not visible. In the lower part, the active layer is deeper than for the Q-N algorithm 465 tomography and presents little lateral heterogeneity that prevent the interpreter from delimitating the 466 landslide layer with accuracy. Globally, the SIRT tomography and the Q-N one are in agreement, but 467 SIRT algorithm does not permit to recover the geotechnical unit limits with the same accuracy and 468 prevents from distinguishing the “Dead body” represented in figure 11b. 469 470 To summarize, we proved that the Q-N algorithm previously developed presented a better horizontal 471 and vertical resolution than the SIRT algorithm (Grandjean and Sage, 2004) and gives the possibility 472 to interpret the bedrock geometry as geomorphological and geological patterns with more details and 473 better resolution than previously. Thanks to the algorithm, we were able to clearly distinguish three of 474 the four geotechnical units proposed by Flageollet et al. (2000). The active unit composed of C1a and 475 C1b geotechnical layers, the “dead body” that represents the C2 layer and the bedrock. 476 477 The seismic attenuation field obtained is in agreement with the P-wave velocities inversed. Although 478 P-wave velocity and seismic attenuation are not linked during the inversion, the attenuation field also 479 permits to distinguish to main materials. The first one presents a relatively low attenuation, that 480 correspond to the bedrock and the “dead body” gathered. The values obtained for this material are 481 around 10-3 Np.m-1, which corresponds to consolidated soils attenuation at 40 Hz (Schön, 1976). The 482 second one is a more attenuating and heterogeneous material that corresponds to the landslide deposit. 483 The attenuation of the landslide layer varies from 4 to 12 10-3 Np.m-1 which are more typical values for 484 unconsolidated soils at this frequency (Schön, 1976). The lateral heterogeneity of the attenuation is 485 important. Areas of high attenuation show attenuation values three times higher than others. The 486 correlation between the SCI and the attenuation is very good, so that we can affirm that attenuation 487 variations are mainly caused by cracking. 488 The seismic wave attenuation tomography highlights two important attenuation zones. The first one, in 489 the upper-part at the abscissas 20-30 seems to be concentrated at the interface between the landslide 490 layer and the bedrock (Fig. 11b). In this area the landslide material undergoes significant shear stresses 491 due to friction between the landslide layer and the bedrock topography. At the surface, cracks wider 492 than 15 cm and measuring several meters in length are visible and the soil is completely remolded. 493 The second zone seems to be associated to the influence of the local bedrock geometry that forms a 494 bump followed by a steep slope (Fig. 11b). Its concave shape is responsible of the tension cracks well 495 visible at the surface and clearly perpendicular to the major change of topography direction (Fig. 3c). 496 Moreover, the soil seems dryer in that zone, certainly because of the geometry of the area that 497 facilitates the drainage of the groundwater table toward lower areas. This phenomenon can even 498 intensify the presence of cracks. 499 We can notice that P-wave velocity and seismic wave attenuation produce complementary results. 500 Only the P-wave velocity tomography can reproduce the sharp geometry of the bedrock topography 501 and differentiate the “dead body” from the bedrock (Fig. 11b). On the other hand, the seismic wave 502 attenuation provides more information on the landslide layer lateral heterogeneity. 503 Here, we can notice that the two high attenuation zones are not correlated with low P-wave 504 velocity as expected (Grandjean et al., 2011). This is explained by the seismic wavepaths going 505 through this weathered material, that are probably too short to impact the velocity, so that only 506 scattering and diffusion effects affect the wave amplitudes. 507 508 Those complementary results highlight the importance of seismic attenuation tomography when characterizing weathering state of soils in near surface application. 509 It is finally important to note that this geophysical method is, in theory, not adapted to image the 510 near surface zone (first meters in depth). Indeed, the poor Fresnel weighs coverage in that zone 511 prevents to obtain high accuracy results. Moreover, cracks and attenuating objects size is certainly 512 comparable or smaller than the cell size (0.67 m). So, we have to be cautious when interpreting those 513 results because the real attenuation zones could be closer to the surface than those presented on the 514 seismic attenuation tomography. 515 516 5. Conclusions 517 518 We present a P-wave tomography inversion algorithm for highly heterogeneous media which 519 combine improvement of resolution and inversion regularization. We use the Fresnel wavepaths 520 calculated for different sources frequencies to retropropagate the traveltime residuals, assuming that in 521 highly heterogeneous media, the first arrivals are affected by velocity anomalies present in the first 522 Fresnel zone through complex multiple scattering. After verifying the ability of the algorithm to 523 recover complex structures on a synthetic dataset, we apply it on a real dataset acquired on the upper 524 part of the Super-Sauze landslide. We verify that our results are in accordance with previous results 525 from Travelletti and Malet (2012) and dynamics penetrometer tests. It appears that the sharp geometry 526 of the bedrock topography is well recovered. This result is of first importance because bedrock 527 topography is one of the main controlling factors of landslide displacement. Using the wavepaths 528 calculated for P-wave velocity tomography inversion, we invert separately the seismic wave 529 attenuation of the same dataset. Although barely applied in landslide environment, we show that with 530 few efforts it was possible to use the amplitude of the first peak of the wave to get an accurate image 531 of the seismic wave attenuation of the landslide layer. The results are in agreement with the observed 532 surface crack inventory and bring complementary information for the construction of an interpreted 533 model. The use of traveltimes and amplitude of waves permit to create an interpreted geological model 534 that gathers those different details. 535 Such geological models are generally created for hazard assessment through numerical modeling. 536 For this work, the use of geophysical tomography is essential because it is the only tool that can 537 provide continuous and integrated imaging of the soil. In this perspective, our algorithm contribution 538 is to answer one of the major issues raised by Travelletti and Malet (2012), namely, the lack of 539 resolution of geophysical tomography compared to geotechnical tests and geomorphological 540 observations. 541 This is why we believe that the Q-N algorithm could really improve the resolution of the 542 geological model, and thus any numerical hydro-mechanical modeling using this variable as a 543 parameter. 544 545 546 6. Acknowledgements 547 548 This work was supported by the French National Research Agency (ANR) within the Project SISCA 549 “’Système Intégré de Surveillance de Crises de glissements de terrains Argileux, 2009-2012” and the 550 BRGM Carnot institute. 551 552 553 554 555 556 557 558 7. References Baina, R.M.H. 1998. Tomographie sismique entre puits : mise en œuvre et rôle de l’analyse à posteriori vers une prise en compte de la bande passante. Phd Thesis. Université Rennes 1, France. Bell, F.G. 2009. Engineering Geology. Second Edition. Elsevier, Oxford. 581p. 559 Bichler, A., Bobrowsky, P., Best, M., Douma, M., Hunter, J., Calvert, T. and Burns, R. 2004. Three- 560 dimensional mapping of a landslide using a multi-geophysical approach: the Quesnel Forks 561 landslide. Landslides, 1(1), 29-40. 562 563 Bruno, F. and Marillier, F. 2000. Test of high-resolution seismic reflection and other geophysical techniques on the Boup landslide in the Swiss Alps. Surveys in Geophysics, 21, 333-348. 564 Ceverny, V. 2001. Seismic ray theory. Cambridge University Press, Cambridge, 713p. 565 Dahlen, F.A., Hung, S.H. and Nolet, G. 2000. Fréchet kernels for finite-frequency traveltimes—I. 566 567 568 Theory. Geophysical Journal International, 141, 157-174. Dahlen, F.A. 2005. Finite-frequency sensitivity kernels for boundary topography perturbations: Geophysical Journal International, 162, 525-540. 569 De Castro Nunes, B.I., de Medeiros, W.E., do Nascimento, A.F. and de Morais Moreira, J.A. 2011. 570 Estimating quality factor from surface seismic data: a comparison of current approaches. Journal of 571 Applied Geophysics, 75, 161-170. 572 Debieche, T.-H., Marc, V., Emblanch, C., Cognard-Plancq, A.-L., Garel, E., Bogaard, T.A. and Malet, 573 J.-P. 2009. Local scale groundwater modelling in a landslide. The case of the Super-Sauze 574 mudslide (Alpes-de-Haute-Provence, France). In: Malet, J.-P., Remaître, A. and Boogard, T.A. 575 (Eds): Proceedings of the International Conference on Landslide Processes: from geomorphologic 576 mapping to dynamic modelling, Strasbourg, CERG Editions, 101-106. 577 578 Flageollet, J.-C., Malet, J.-P. and Maquaire, O. 2000. The 3D Structure of the Super-Sauze Earthflow: A first stage towards Modelling its Behavior. Physics and Chemistry of the Earth, 25, 785-791. 579 Glade, T., Stark, P. and Dikau, R. 2005. Determination of potential landslide shear plane depth using 580 seismic refraction. A case study in Rheinhessen, Germany. Bulletin of Engineering Geology and 581 the Environment, 64, 151-158. 582 Grandjean, G. and Sage, S. 2004. JaTS: a fully portable seismic tomography software based on Fresnel 583 wavepaths and a probabilistic reconstruction approach. Computers and Geosciences, 30, 925-935. 584 Grandjean, G., Pennetier, C., Bitri, A., Meric, O. and Malet, J.-P. 2006. Caractérisation de la structure 585 interne et de l’état hydrique de glissements argilo-marneux par tomographie géophysique : 586 l’exemple du glissement-coulée de Super-Sauze (Alpes du Sud, France). Comptes Rendus 587 Geosciences, 338, 587-595. 588 Grandjean, G., Malet, J.-P., Bitri, A. and Méric, O. 2007. Geophysical data fusion by fuzzy logic for 589 imaging the mechanical behavior of mudslides. Bulletin Société Géologique de France, 177(2), 590 127-136. 591 Grandjean, G., Gourry, J.-C., Sanchez, O., Bitri, A. and Garambois, S. 2011. Structural study of the 592 Ballandaz landslide (French Alps) using geophysical imagery. Journal of Applied Geophysics, 75, 593 531-542. 594 Grandjean, G., Bitri, A. and Krzeminska, M. 2012. Characterization of a landslide fissure pattern by 595 integrating seismic azimuth tomography and geotechnical testing. Hydrological Processes. (in 596 press). 597 598 599 600 Hagedoorn, J.G. 1959., The plus-minus method of interpreting seismic refraction sections. Geophysical Prospecting, 7(2), 158-182. Jongmans, D. and Garambois, S. 2007. Geophysical investigation of landslides: a review. Bulletin Société Géologique de France, 178(2), 101-112. 601 Kissling, E., Husen, S. and Haslinger, F. 2001. Model parameterization in seismic tomography: a 602 choice of consequence for the solution quality. Physics of the Earth and Planetary Interiors, 123, 603 89-101. 604 605 Liu, Y., Dong, L., Wang, Y., Zhu J. and Ma, Z. 2009. Sensitivity kernels for seismic Fresnel volume tomography. Geophysics, 74, U35-U46. 606 Malet, J.-P., Auzet, A.-V., Maquaire, O., Ambroise, B., Descroix, L., Estèves, M., Vandervaere, J.-P. 607 and Truchet E. 2003. Soil surface characteristics influence on infiltration in black marls: 608 application to the Super-Sauze earthflow (Southern Alps, France). Earth Surface Processes and 609 Landforms, 28, 547-564. 610 611 Malet, J.-P., Laigle, D., Remaître, A. and Maquaire, O. 2005a. Triggering conditions and mobility of debris-flows associated to complex earthflows. Geomorphology, 66(1-4): 215-235. 612 Malet, J.-P., van Asch, Th.W.J., Van Beek, L.P.H. and Maquaire O. 2005b. Forecasting the behaviour 613 of complex landslides with a spatially distributed hydrological model. Natural Hazards and Earth 614 System Sciences, 5, 71-85. 615 Maquaire, O., Malet, J.-P., Remaître, A., Locat, J., Klotz, S. and Guillon, J. 2003. Instability 616 conditions of marly hillslopes: towards landsliding of gullying? The case of the Barcelonnette 617 Basin, South East France. Engineering Geology, 70, 109-103. 618 Mauritsch, H.J., Seiberl, W., Arndt, R., Römer, A., Schneiderbauer, K. and G.P. Sendlhofer 2000. 619 Geophysical investigations of large landslides in the Carnic Region of southner Austria. 620 Engineering Geology, 56, 373-388. 621 622 623 624 625 626 627 628 Nolet, G. 1985. Solving or resolving inadequate and noisy tomographic systems. Joumal of Computational Physics, 61, 463-482. Nolet, G. 1987. Seismic wave propagation and seismic tomography. In: Nolet, G. (Ed.), Seismic Tomography, Reidel, Dordrecht, 1-23. Paige, C. and Saunders, M. 1982. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Transaction on Mathematical Software, 8, 43-71. Palmer, D. and Burke-Kenneth, B.S. 1980. The generalized reciprocal method of seismic refraction interpretation. Society of Exploration Geophysicists. Tulsa, 104 p. 629 Podvin, P. and Lecomte, I. 1991. Finite difference computation of traveltimes in very contrasted 630 velocity model: a massively parallel approach and its associated tools. Geophysical Journal 631 International, 105, 271-284. 632 Popovici, M. and Sethian, J. 1998. Three dimensional traveltimes using the fast marching method. In: 633 Hassanzadeh, S. (Ed) : Proceedings SPIE 3453, Mathematical Methods in Geophysical Imaging V, 634 82p. 635 636 637 638 Pratt, R.G. 1999. Seismic waveform inversion in the frequency domain. Part 1: Theory and verification in a physic scale model. Geophysics, 64, 888-901. Romdhane, A., Grandjean, G., Brossier, RM, Réjiba, F., Operto, S. and Virieux, J. 2011. Shallowstructure characterization by 2D elastic full-waveform inversion. Geophysics, 76, 81-93. 639 Schmutz, M., Albouy, Y., Guérin, R., Maquaire, O., Vassal, J., Schott, J.-J. and Descloîtres, M. 2000. 640 Joint electrical and time domain electromagnetism (TDEM) data inversion applied to the Super- 641 Sauze earthflow (France). Surveys in Geophysics, 21, 371-390. 642 643 644 645 646 647 648 649 Schön, J.H. 1976. The physical properties of rocks: fundamentals and principles of petrophysics. Pergamon, New York, 601p. Schrott, L. and Sass, O. 2008 Application of field geophysics in geomorphology: Advances and limitations exemplified by case studies. Geomorphology, 93, 55-73. Sirgue, L. and Pratt, R.G. 2004. Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies. Geophysics, 69, 231-248. Spetzler, J. and Snieder, R. 2004. The Fresnel volume and transmitted waves. Geophysics, 69, 653663. 650 Spetzler, J., Xue, Z., Saito, H. and Nishizawa, O. 2008. Case story: Timelapse seismic crosswell 651 monitoring of CO2 injected in an onshore sandstone aquifer. Geophysical Journal International, 652 172, 214-225. 653 654 655 656 Sun, J., Sun, Z. and Han, F. 2011. A finite difference scheme for solving the eikonal equation including surface topography. Geophysics 76, T53. Tarantola, A. 1987. Inverse problem theory. Methods for data fitting and model parameters estimation. Society of Industrial and Applied Mathematics, Philadelphia, 342p. 657 Trampert, J. and Lévèque J.-J. 1990. Simultaneous iterative reconstruction technique: Physical 658 interpretation based on the generalized Least Squares solution. Journal of Geophysical Research, 659 95, 553-559. 660 Travelletti, J. and Malet, J.-P. 2012. Characterization of the 3D geometry of flow-like landslides: A 661 methodology based on the integration of heterogeneous multi-source data. Engineering Geology, 662 128, 30-48. 663 van Asch, Th.W.J., Malet, J.-P. and van Beek, L.H.P. 2006. Influence of landslide geometry and 664 kinematic information to describe the liquefaction of landslides: Some theoretical considerations. 665 Engineering Geology, 88, 59-69. 666 667 van Dam, R.L. 2010. Landform characterization using geophysics—Recent advances, applications, and emerging tools. Geomorphology. In press. 668 van der Sluis, A. and van der Vorst, H.A. 1987. Numerical solutions of large, sparse linear systems 669 arising from tomographic problems. In: Nolet, G. (Ed): Seismic Tomography with Applications in 670 Global Seismology and Exploration Geophysics, Reidel, Dordrecht, 53-87. 671 672 673 674 675 676 677 678 Vasco, D.W., Peterson, J.E. and Majer, E.L. 1995. Beyond ray tomography: Wavepaths and Fresnel volumes. Geophysics, 60, 1790-1804. Vidale, J. 1988. Finite-difference calculation of travel time. Bulletin Seismological Society of America, 78, 2062-2076. Virieux, J. and Operto, S. 2009. An overview of full waveform inversion in exploration geophysics. Geophysics, 74(6), WCC1-WCC26. Watanabe, T. and Sassa, K. 1996. Seismic attenuation Tomography and its application to rock mass evaluation. International Journal of Rock Mechanics and Mining Sciences, 33(5), 467-477. 679 Watanabe, T., Matsuoka, T. and Ashida Y. 1999. Seismic traveltime tomography using Fresnel 680 volume approach. 69th Proceedings, Society Exploration Geophysics, Houston, USA, SPRO12.5. 681 Yomogida, K. 1992. Fresnel zone inversion for lateral heterogeneities in the Earth. Pure and Applied 682 Geophysics, 138, 391-406. 683 Zelt, C.A. and Barton, P.J. 1998. Three-dimensional seismic refraction tomography: A comparison of 684 two methods applied to data from the Faeroe Basin. Journal of Geophysical Research, 103(B4), 685 7187-7210. 686 687 688 689 690 691 692 693 Zhao, H. 2005. A fast sweeping method for eikonal equations. Mathematics of Computation, 74, 603627. Zhao, L., and Jordan, T.H. 2006. Structural sensitivities of finite-frequency seismic waves: A fullwave approach. Geophysical Journal International, 165, 981-990. 694 695 Figure Captions 696 697 698 Figure 1: Fresnel weights (e.g. distance versus depth) computed for a medium characterized by a 699 constant velocity of 500 m.s-1 and for three frequencies: a) 100 Hz, b) 200 Hz and c) 300Hz. The 700 source is located at x=0 m and the receptor at x=25m, both at 12.5 m of depth. 701 702 703 704 Figure 2: Algorithm validation on a synthetic dataset: a) Synthetic initial model, b) Final velocity 705 model inverted with the SIRT algorithm, c) Final velocity model inverted with the Q-N algorithm. 706 Vertical cross-sections extracted from the three models at a distance of 46 m d), 110 m e) and 145 m 707 f). 708 709 710 711 Figure 3: Location of the investigated area within the Super-Sauze landslide. The seismic profile 712 (red) is represented on an orthophotograph overlaid on a digital elevation model of the landslide. The 713 main scarp and the landslide limit. Picture a) shows the seismic device on the field. Picture b) and c) 714 represent the observed fissure state of the soil along the profile. 715 716 717 Figure 4: Data quality: a) Seismic shot# 13. b) Source amplitude spectrum of the total seismic shot (blue) and source amplitude spectrum of the P-wave of the selected area (red). 718 719 720 Figure 5: Picking quality: Frequency distribution of differential traveltime errors (e.g. due to 721 reciprocal differences). The standard deviation has a value of 2.2047 ms for 427 tested reciprocal 722 traveltimes. The grey color indicates the data rejected in the inversion process. 723 724 725 726 Figure 6: Example of vertical P-wave velocity profile for the seismic shot #4: a) Slant-stack 727 transformation in the t-v (time-velocity) domain for the seismic shot #4, b) Estimated vertical velocity 728 profile for each t0, c) Vertical velocity profile inverted for the shot #4. 729 730 731 732 733 Figure 7: Misfit function values for the Q-N and SIRT algorithms. 734 735 736 Figure 8: Inversion results of the real dataset acquired on the Super-Sauze landslide: a) initial 737 velocity model, b) inverted model with the SIRT algorithm of Grandjean and Sage (2004), and c) 738 inverted model with the Q-N algorithm. 739 740 741 742 743 744 Figure 9: Seismic wave attenuation tomography: a) Surface Craking Index (SCI) and b) attenuation section inverted from the Super-Sauze data. 745 746 747 Figure 10: Comparison of the bedrock geometry interpreted with the Q-N algorithm and with a 748 geological modeler by integration of multi-source information at coarser spatial resolution (Travelletti 749 and Malet, 2012) in terms of bedrock depth a) and layer thickness b). 750 751 752 753 Figure 11: a) Pre-event topography before the landslide and location of the seismic profile, b) 754 Interpreted geological cross-section in 3 layers: the active unit corresponds to the moving landslide 755 layer, the dead body is a compacted and quasi-impermeable layer showing low displacements and the 756 bedrock constituted of in-situ black marls.